Crossover from quantum to thermal behaviour in quantum spin liquids.

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Quantum spin liquids (QSLs) host a variety of exotic phenomena including fractionalisation, nontrivial braiding statistics of excitations, and the absence of long range order. While a number of candidate materials have been proposed, experimental detection of QSLs remains challenging due to the lack of any local order parameter. As part of the search for a `smoking gun' experimental signature, it is crucial to obtain a detailed understanding of the expected features characteristic of QSLs in well-established experimental techniques, including neutron scattering and NMR. We must therefore understand the interplay of spin liquid behaviour and the unavoidable presence of temperature, both at the theoretical level, and in terms of determining further potential experimental implications.Experimentally, the key characteristic of topologically ordered phases is their fractionalised excitations, such as the Laughlin quasiparticles of the fractional quantum Hall effect, or the magnetic monopoles of spin ice. At finite temperature, a finite density of these excitations will be excited thermally. This goal of this project is to study the effect that these excitations have on key system properties. First, we consider the entanglement content, as quantified by the logarithmic negativity, a recently proposed measure of mixed state entanglement. We show how an O(1) density of thermally excited quasiparticles leads to the demise, and eventually sudden death, of quantum correlations. In addition, we will study the dynamics of anyons at nonzero temperature. In particular, we hope to explore how the motion of one species of particle is affected by a background of thermally excited quasiparticles of a different species, when the two species obey nontrivial mutual braiding statistics. The long term goal of the project is to understand the effect of temperature on QSLs in general, with a particular focus on obtaining signatures of the T=0 QSL state in experimental data at nonzero temperatures.